Carbonates contain more than 50% of the world's known hydrocarbon resources. Although natural fractures are a common feature in carbonates and they can improve primary production from tight matrix carbonates, they pose a unique challenge for enhanced oil recovery (EOR) from heavy oil and bitumen (HOB) carbonates. The current focus on ‘energy mix’ to sustain the world energy demand has once again put HOB carbonates in global spotlight. Among the known HOB carbonate reservoirs globally, the Grosmont carbonate in Northern Alberta contains the largest original in-place HOB (~406.5 billion barrels). However, the Grosmont carbonate poses the greatest development challenge of all other known HOB carbonates due to its petrophysical complexity. We recently published our progress towards developing a methodology for characterizing the Grosmont carbonate that is suitable for direct reservoir simulation. The objective of the current paper is to assess the performances of different steam-based EOR recovery technologies using multiobject reservoir models of the Grosmont. Our results show that simulations on appropriate reservoir models representative of the most hydraulically active objects produce a good account of heat and fluid flow in complex carbonates. Cyclic steam stimulation (CSS) in this paper describes steam injection below fracture pressure and can therefore be related to what has recently been presented in the literature as cyclic single well steam-assisted gravity drainage.